On Symmetries and Conservation Laws of the Majda-Biello System

Vodova-Jahnova, Jirina

doi:10.48550/arxiv.1405.7858

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We believe that using the technique similar to that of [43] (cf. also [20,44]) it can be shown that in the case of n = −5 equation ( 13) admits no genuinely generalized symmetries, including those with explicit dependence on T and not just the time-independent ones whose nonexistence follows from the above comparison of ( 15) with ( 23), so we are left with just one integrable case of n = −2 which we discuss below.…”

Section: Integrabilitymentioning

confidence: 99%

Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules

Sergyeyev

Skurativskyi

Vladimirov

2019

Nonlinear Analysis: Real World Applications

View full text Add to dashboard Cite

We present the results of study of a nonlinear evolutionary PDE (more precisely, a oneparameter family of PDEs) associated with the chain of pre-stressed granules. The PDE in question supports solitary waves of compression and rarefaction (bright and dark compactons) and can be written in Hamiltonian form. We investigate inter alia integrability properties of this PDE and its generalized symmetries and conservation laws.For the compacton solutions we perform a stability test followed by the numerical study. In particular, we simulate the temporal evolution of a single compacton, and the interactions of compacton pairs. The results of numerical simulations performed for our model are compared with the numerical evolution of corresponding Cauchy data for the discrete model of chain of pre-stressed elastic granules.

show abstract

Section: Integrabilitymentioning

confidence: 99%